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A Comparison of Strategies for the Automatic Computation of Two-Dimensional Integrals over Infinite Domains

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Abstract

We present sets of parameterized integral test families over each of the domains [0,∞)2 and (−∞,∞)2, exhibiting various rates of integrand decay, and use these families to compare the performances of the two general-purpose two-dimensional cubature algorithms r2d2lri and Cubpack++ for integration over such nonfinite domains. The data collected for this comparison is helpful in identifying the respective advantages and disadvantages of the strategies adopted by the two algorithms when dealing with nonfinite domains.

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References

  1. R. Cools and A. Haegemans, Construction of fully symmetric cubature formulae of degree 4k -3 for fully symmetric planar regions, J. Comput. Appl. Math. 17 (1987) 173–180.

    Google Scholar 

  2. R. Cools, D. Laurie and L. Pluym, Algorithm 764: Cubpack++: A C++ package for automatic two-dimensional cubature, ACM Trans. Math. Software 23(1) (1997) 1–15.

    Google Scholar 

  3. A.C. Genz, Testing multidimensional integration routines, in: Tools, Methods and Languages for Scientific and Engineering Computation, eds. B. Ford, J.C. Rault and F. Thomasset (North-Holland, Amsterdam, 1984) pp. 81–94.

    Google Scholar 

  4. A.C. Genz, A package for testing multiple integration subroutines, in: Numerical Integration: Recent Developments, Software and Applications, eds. P. Keast and G. Fairweather (Reidel, Dordrecht, 1987) pp. 337–340.

    Google Scholar 

  5. M. Hill and I. Robinson, d2lri: A non-adaptive algorithm for two-dimensional cubature, J. Comput. Appl. Math. 112 (1999) 121–145.

    Google Scholar 

  6. I. Robinson and M. Hill, r2d2lri: An algorithm for automatic two-dimensional cubature, ACM Trans. Math. Software 27(3) (2001) 73–89.

    Google Scholar 

  7. A. Sidi, A new variable transformation for numerical integration, in: International Series of Numerical Mathematics, Vol. 112 (1993) pp. 359–373.

    Google Scholar 

  8. I.H. Sloan and S. Joe, Lattice Methods for Multiple Integration (Clarendon Press, Oxford, 1994).

    Google Scholar 

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Authors and Affiliations

  1. La Trobe University, Victoria, 3086, Australia

    Michael Hill & Ian Robinson

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  1. Michael Hill
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  2. Ian Robinson
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Hill, M., Robinson, I. A Comparison of Strategies for the Automatic Computation of Two-Dimensional Integrals over Infinite Domains. Numerical Algorithms 34, 325–338 (2003). https://doi.org/10.1023/B:NUMA.0000005348.15222.6a

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  • DOI: https://doi.org/10.1023/B:NUMA.0000005348.15222.6a

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